Re: Does linearly dependent imply statistically dependent?

In article <1115270959.241138.48700@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<wangxu78@xxxxxxxxx> wrote:
>Then whether the following statement is true?

>If X, Y, and Z have non-degenerate continuous distribution, and they
>are statistically independent, then
>X, Y and Z cannot be linearly dependent.

Wrong. If X, Y, and Z has a non-planar distribution,
they cannot be linearly dependent. But a planar
distribution can be continuous and non-degenerate.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

Relevant Pages

  • Re: Lilliefors Test : 40 years
    ... The Lilliefors Test tests whether a distribution is ... and unknown mean, known mean and unknown variance, ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.stat.math)
  • Re: help: testing for unimodality in multiple dimensions?
    ... >continuous distribution. ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.stat.consult)
  • Re: Kolmogorov-Smirnov test... a good overview
    ... the distribution of the KS ... of statistics is "self-thought" with applications in mind. ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.stat.math)
  • Re: non parametric "functions"
    ... >such a concept as a "non parametric function"? ... also known as a distribution free ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.math)
  • Re: Testing for product of Gaussians
    ... >I have a value created by a computer simulation. ... test against the computed Bessel function distribution will ... I know the answer to the diffusion equation, ... are those of the Statistics Department or of Purdue University. ...
    (sci.math)